Production RL pipelines for large language models routinely violate the on-policy assumption along three independent axes. Partial rollouts resume long chain-of-thought trajectories after a parameter update. Rollout replay re-injects past successful trajectories. Asynchronous training decouples sampling from optimization, so trajectories arrive several updates stale. Today these biases are absorbed by a single, theoretically unjustified instrument: a token-level PPO clip whose magnitude is invariant to the actual policy divergence. We show that all three regimes are instances of one mathematical object: a trajectory composed of segments produced by distinct behavior policies. Building on this view, we introduce **SPIRE** (**Segment-wise Prefix Importance with Replay Equilibrium**), a drop-in replacement for the policy-gradient estimator in GRPO-style optimizers. **SPIRE** is: 1. **Unbiased** under a prefix-measurable boundary condition; 2. **Variance-controlled**, admitting a tight per-segment second-moment bound via Renyi-2 divergence with a closed-form MSE-optimal clip; 3. **Replay-equilibrium aware**, admitting a closed-form Pareto-optimal replay/fresh mixing ratio from a KKT analysis of the constrained MSE/throughput problem. On Qwen2.5-Math-1.5B, Qwen2.5-7B, and Llama-3.1-8B trained with verifiable rewards on MATH-500, AIME-2024, OlympiadBench, LiveCodeBench-v5, and GPQA-D, **SPIRE** delivers **+3.6 to +6.8 absolute points on AIME-2024** and **+2.1 to +4.4 on OlympiadBench** at iso-FLOPs, while remaining stable up to **4x trainer/sampler staleness**, where AReaL+PPO collapses. Baselines marked with a double-dagger symbol are reproduced verbatim from the corresponding paper on the matching model-benchmark pair; **SPIRE** numbers reflect the model’s own runs released with this submission.